Recommendations on replicating an RDS PostgreSQL instance?

I think that pglogical extension could be be used to solve your issue - in the future, when it is extended to allow a replication user. Currently it requires superuser privileges.

pglogical is a logical replication system implemented entirely as a PostgreSQL extension.

Also, from their documentation:

Fully integrated, it requires no triggers or external programs. This alternative to physical replication is a highly efficient method of replicating data using a publish/subscribe model for selective replication.

Use cases supported are:

• Upgrades between major versions (given the above restrictions)
• Full database replication
• Selective replication of sets of tables using replication sets
• Data gather/merge from multiple upstream servers